These links might help you determine which zone you are in. Different zones use different criteria, but they mainly look at freezing or frost dates in your area. Freezing and frost dates are different. We all have our own microclimates in the zones, so they are just approximations, but you will often notice a zone in the write-up of plant descriptions, especially trees. According to these three, I live in three different zones, 6, 7, and 7A. I'm right on the border and these three obviously use different criteria, but I know I should never plant a tree that will not do well in both zones 6 and 7.
Arbor Day Zip Code Planting Zone
http://www.arborday.org/treeinfo/zonelookup.cfm
Zip Code Planting Zone
http://www.gardenweb.com/zones/zip.cgi
Zip Code Planting Zone
http://www.garden.org/zipzone/
I do not mulch squash and zucchini since that gives the squash bug (not the squash borer, the squash bug that looks a lot like a stink bug) a place to hide. Besides, once they get started, they pretty much shade out the weeds anyway. You do need to keep them cleaned of weeds and grass until they get started though. The squash bugs do not bother my cucumbers, so they can be mulched. I don't know if the squash bugs bother cantaloupe, pumpkin, or watermelon. I would think you can mulch them and they would greatly benefit, but I don't grow them. They take up too much room for me.
I direct sow my leaf lettuce, radishes and carrots and do not mulch them. You'll probably need to weed them once, at most twice for the lettuce and carrots, then they should shade out about everything else.
The tomatoes, peppers, sugar snap peas bush type, green beans bush type, cauliflower, broccoli, and head lettuce can all be mulched if you wish. I've done the peas, beans, cauliflower, and broccoli both ways. I've never grown head lettuce but it should be about the same as broccoli and cauliflower. The peas, broccoli and cauliflower are not long producing plants and, once they get going, they pretty keep the weeds down. I think mulch helps them in a couple of ways other than keeping the weeds down. The are cool weather plants and mulch helps keep the soil cool if you use lighter colored mulch. Dark mulch will warm up the soil. They also greatly benefit from keeping the soil moist but not soaking wet. Mulch helps keep moisture in. Keeping the moisture relatively stable is a great benefit.
I think it is important that you do mulch tomatoes and peppers. They should produce over a long period of time in your area. Once they get going good, it is hard to keep the weeds out without damaging the plants, they grow so big. Constant moisture helps reduce splitting of the tomatoes after a rain. If the ground is dry, then it rains, tomatoes will soak up so much moisture that it splits the tomatoes. It still happens with me, but the mulch helps some.
The main reason I think it is important to mulch tomatoes and peppers is that they can get a blight that can greatly reduce production or even kill the plants. This blight gets splashed up on the plant from the soil when it rains or maybe when you water. If you have a layer of mulch it keeps the soil from splashing up on your plant.
There are several different ways to support tomatoes; stakes, trellises, and cages to name the basics, but there are many variations of each. A stake is one dimensional, having height but no width or length. A trellis is two dimensional, having height and length but no width. A cage has all three dimensions. The tomatoes will compete with each other for sunlight. As long as you can figure out how to let them all have sufficient sunlight, there is no harm in letting them share a trellis or cage. The disclaimer to this is that if one tomato plant gets diseased, say blight from the soil, the disease can spread through all the tomatoes much easier if they are touching each other than if they are separately supported. I tend to trellis or cage my tomatoes together.
I also trellis my cucumbers. They take up less space and are easier to keep the weeds down if they are trellised.
We all do things differently and have different climates and conditions. Hopefully some of this will help you in your specific conditions.
. The plants compete for water, nutrients, and, very importantly, sunlight.
